Analysis of covariance (ANCOVA) using polynomial chaos expansions

ABSTRACT: Global sensitivity analysis aims at quantifying the uncertainty of the output of a computer model that may be attributed to each input parameter or combination thereof. Variance decomposition tech-niques that lead to the well-known Sobol ’ indices are now well established. However this classical framework only holds for independent input parameters. Moreover, when the computational model under consideration is costly to evaluate, it is not possible to resort to crude Monte Carlo simulation to evaluate sensitivity indices. In this paper we extend the polynomial chaos-based Sobol ’ indices derived by Sudret (2006, 2008) to the case of dependent input parameters using the covariance decomposition recently proposed by Li et al.. The functional decomposition which is natively given by the polynomial chaos expansion is taken advantage of, and the pro-posed approach is consistent with the classical Sobol ’ indices when the input variables are independent. The methodology is illustrated on a tolerance analysis problem. 1